Risk-adjusted monitoring of survival times.

We consider the monitoring of surgical outcomes, where each patient has a different risk of post-operative mortality due to risk factors that exist prior to the surgery. We propose a risk-adjusted (RA) survival time CUSUM chart (RAST CUSUM) for monitoring a continuous, time-to-event variable that may be right-censored. Risk adjustment is accomplished using accelerated failure time regression models. We compare the average run length performance of the RAST CUSUM chart with the RA Bernoulli CUSUM chart using data from cardiac surgeries to motivate the details of the comparison. The comparisons show that the RAST CUSUM chart is more efficient at detecting a sudden increase in the odds of mortality than the RA Bernoulli CUSUM chart, especially when the fraction of censored observations is relatively low or when a small increase in the odds of mortality occurs. We also discuss the impact of the amount of training data used to estimate chart parameters as well as the implementation of the RAST CUSUM chart during prospective monitoring.

Detecting a rate increase using a Bernoulli scan statistic.

Scan statistics are used in public health applications to detect increases in rates or clusters of disease indicated by an unusually large number of events. Most of the work has been for the retrospective case, in which a single set of historical data is to be analyzed. A modification of this retrospective scan statistic has been recommended for use when incidences of an event are recorded as they occur over time (prospectively) to determine whether the underlying incidence rate has increased, preferably as soon as possible after such an increase. In this paper, we investigate the properties of the scan statistic when used in prospective surveillance of the incidence rate under the assumption of independent Bernoulli observations. We show how to evaluate the expected number of Bernoulli observations needed to generate a signal that the incidence rate has increased. We compare the performance of the prospective scan statistic method with that obtained using the Bernoulli-based cumulative sum (CUSUM) technique. We show that the latter tends to be more effective in detecting sustained increases in the rate, but the scan method may be preferred in some applications due to its simplicity and can be used with relatively little loss of efficiency.

A comparison of surveillance methods for small incidence rates.

A number of methods have been proposed for detecting an increase in the incidence rate of a rare health event, such as a congenital malformation. Among these are the sets method, two modifications of the sets method, and the CUSUM method based on the Poisson distribution. We consider the situation where data are observed as a sequence of Bernoulli trials and propose the Bernoulli CUSUM chart as a desirable method for the surveillance of rare health events. We compared the performance of the sets method and its modifications with that of the Bernoulli CUSUM chart under a wide variety of circumstances. Chart design parameters were chosen to satisfy a minimax criteria. We used the steady-state average run length to measure chart performance instead of the average run length (ARL), which was used in nearly all previous comparisons involving the sets method or its modifications. Except in a very few instances, we found that the Bernoulli CUSUM chart has better steady-state ARL performance than the sets method and its modifications for the extensive number of cases considered. Thus, we recommend the use of the Bernoulli CUSUM chart to monitor small incidence rates and provide practical advice for its implementation.